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MEMS 424 matlab

创建日期：2024-05-25 17:47:18

所属分类：数学mathematics

标签： MEMS 424

matlab

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MEMS 424 Finite Element Methods Final Project

This final project will be an individual report. We have focused our efforts in this class on understanding
the math involved in the finite-element method (FEM), but this final project will be an analysis using
commercial software to do a structural analysis of a real-world type of problem. Some students may
choose to do a project involving writing custom software in Matlab or another programming language.
Project Description
Please choose a ‘real world’ structure to analyze. This could be a part of a piece of furniture, an
automotive part, a part on a bicycle, or any other physical structure that could fail under load. You will
analyze this part using commercial FEM software. You may use Comsol Multiphysics, as that is what we
have used for the labs, but you are also welcome to use another package such as Ansys Mechanical,
Abaqus, StressCheck, or Nastran. Do not use SW simulation here, as it is a somewhat limited software,
and I would like those who are familiar with it to branch out to other software.
Report format and sections
Cover sheet
Please include a cover sheet with the following information:
• University Name
• Department name
• Class Name
• Report title (such as ‘Finite-Element Analysis of a …’)
• Your Name
• Date
Problem description
The first section of your report should describe the problem. At a minimum, this should include the
following information:
• A drawing of the part you are analyzing with dimensions
• A drawing showing the physical loads and constraints being applied to the part (this can be
combined with the drawing above if it is convenient, or shown separately)
• Material properties used in the analysis
• Values of loads used in the analysis
• A list of all assumptions used in the analysis (such as linear material properties, small
deformations, static loading, etc.)
• A brief description of the problem being analyzed. This could describe the following aspects of
the problem:
o What is the part you are analyzing?
o What are the real-world load cases you are modeling?
o What are the possible modes of failure? (exceeding yield stress, excessive deflection,
excitation at resonant frequencies)
Analysis methods
• What software are you using?
MEMS 424 Finite Element Methods Final Project - SP2023
• Are you using 2D (plane stress, plane strain???) / 3D? Both (2D then 3D?)
• How are you modeling the real-world loads? (Describe the possible real world loading and then
show how you modeled it in software. You may try different approaches to applying the loads)
• How are you modeling the constraints? (Again, what is the real-world situation and how are you
modeling that in the FEM software?)
• What type of mesh are you using?
o What kind of elements – triangular, quadrilateral, tetrahedral, pentahedral, hexahedral?
o What order shape functions are you using?
o How many elements did you use (or how many DOF did you use?). If multiple runs with
different meshes were used, give the range of values used.
o Did you use localized mesh refinement?
• Show representative images (screenshots) to visualize boundary conditions and mesh as
appropriate.
Analysis results
Show images of the results of the analysis. These may be plots of von Mises stress, 1st principal stress,
displacements, vibration mode shapes (if appropriate). Show zoomed in images at locations of
maximum stress.
Show evidence that you have checked the following conditions:
• The deformations observed are consistent with the applied loadings
• Values obtained are physically reasonable (For example: Is there an analytical check you can do?
Do deflections seem physically reasonable? Are stresses below yield limit or fatigue limit? What
is your factor of safety?)
• The mesh is sufficiently resolved so that the solution does not change dramatically as the mesh
is changed.
o Show that secondary quantities such as stresses vary smoothly across elements at stress
concentrations
o Show that local quantities of interest (stress at a fillet for instance) do not change
dramatically as the mesh is resolved (show at least one mesh convergence study)
Discussion
What are the takeaways from this analysis?
• Is the structure predicted to fail under the loading / constrain conditions?
• Does it fail in some load cases and not others?
• What are the modes of failure in which it fails?
• Are there improvements that could be made to the structure to improve its performance (make
it lighter for instance) or make it safer (areas that should be reinforced)?
• What are the limitations of your model? Are there physical phenomena or uncertainties that
this model does not capture? Are there other ways the part could fail that you were not able to
model?
• How confident are you in your predictions and why?
• What physical tests would you recommend to validate your results or calibrate your model
(determine unknown parameters in the model)?
MEMS 424 Finite Element Methods Final Project - SP2023
• Are there any other aspects of the analysis or suggestions for future analysis that you feel are
worth discussing?

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